The use of quadrupole electrode systems in mass spectrometers is known. For example, U.S. Pat. No. 2,939,952 (Paul et. al.) describes a quadrupole electrode system in which four rods surround and extend parallel to a central axis. Opposite rods are coupled together and brought out to one of two common terminals. Most commonly, an electric potential V(t)=+(U−V cos Ωt) is then applied between one of these terminals and ground and an electric potential V(t)=−(U−V cos Ωt) is applied between the other terminal and ground. In these formulae, U is the DC voltage, pole to ground, and V is the zero to peak radio frequency (RF) voltage, pole to ground.
In constructing a linear quadrupole, the field may be distorted so that it is not an ideal quadrupole field. For example round rods are often used to approximate the ideal hyperbolic shaped rods required to produce a perfect quadrupole field. The calculation of the potential in a quadrupole system with round rods can be performed by the method of equivalent charges—see, for example, Douglas et al., Russian Journal of Technical Physics, 1999, Vol. 69, 96-101. When presented as a series of harmonic amplitudes A0, A1, A2 . . . An, the potential in a linear quadrupole can be expressed as follows:                               ϕ          ⁡                      (                          x              ,              y              ,              z              ,              t                        )                          =                                            V              ⁡                              (                t                )                                      ×                          ϕ              ⁡                              (                                  x                  ,                  y                                )                                              =                                    V              ⁡                              (                t                )                                      ⁢                                          ∑                n                                                                               ⁢                                                ϕ                  n                                ⁡                                  (                                      x                    ,                    y                                    )                                                                                        (        1        )            
Field harmonics φhd n, which describe the variation of the potential in the X and Y directions, can be expressed as follows:                                           ϕ            n                    ⁡                      (                          x              ,              y                        )                          =                  Real          ⁢                                           [                                                    A                n                            ⁡                              (                                                      x                    +                                          ⅈ                      ⁢                                                                                           ⁢                      y                                                                            r                    0                                                  )                                      2                    ]                                    (        2        )            For example:                                           ϕ            0                    ⁡                      (                          x              ,              y                        )                          =                                            A              0                        ⁢                          Real              ⁢                                                           [                                                (                                                            x                      +                                              ⅈ                        ⁢                                                                                                   ⁢                        y                                                                                    r                      0                                                        )                                0                            ]                                =                                    A              0                        ⁢                                                   ⁢            Constant            ⁢                                                   ⁢            potential                                              (        3        )                                                      ϕ            2                    ⁡                      (                          x              ,              y                        )                          =                                            A              2                        ⁢                          Real              ⁢                                                           [                                                (                                                            x                      +                                              ⅈ                        ⁢                                                                                                   ⁢                        y                                                                                    r                      0                                                        )                                2                            ]                                =                                                    A                2                            ⁡                              (                                                                            x                      2                                        -                                          y                      2                                                                            r                    0                    2                                                  )                                      ⁢                                                   ⁢            Quadrupole                                              (        4        )                                                      ϕ            4                    ⁡                      (                          x              ,              y                        )                          =                                            A              4                        ⁢                          Real              ⁢                                                           [                                                (                                                            x                      +                                              ⅈ                        ⁢                                                                                                   ⁢                        y                                                                                    r                      0                                                        )                                4                            ]                                =                                                    A                4                            ⁡                              (                                                                            x                      4                                        -                                          6                      ⁢                                              x                        2                                            ⁢                                              y                        2                                                              +                                          y                      4                                                                            r                    0                    4                                                  )                                      ⁢                                                   ⁢            Octopole                                              (        5        )                                                      ϕ            6                    ⁡                      (                          x              ,              y                        )                          =                                            A              6                        ⁢                          Real              ⁢                                                           [                                                (                                                            x                      +                                              ⅈ                        ⁢                                                                                                   ⁢                        y                                                                                    r                      0                                                        )                                6                            ]                                =                                                    A                6                            ⁡                              (                                                                            x                      6                                        -                                          15                      ⁢                                              x                        4                                            ⁢                                              y                        2                                                              +                                          15                      ⁢                                              x                        2                                            ⁢                                              y                        4                                                              -                                          y                      6                                                                            r                    0                    6                                                  )                                      ⁢                                                   ⁢            Dodecapole                                              (        5.1        )                                                      ϕ            8                    ⁡                      (                          x              ,              y                        )                          =                                            A              8                        ⁢                          Real              ⁢                                                           [                                                (                                                            x                      +                                              ⅈ                        ⁢                                                                                                   ⁢                        y                                                                                    r                      0                                                        )                                8                            ]                                =                                                    A                8                            ⁡                              (                                                                            x                      8                                        -                                          28                      ⁢                                              x                        6                                            ⁢                                              y                        2                                                              +                                          70                      ⁢                                              x                        4                                            ⁢                                              y                        4                                                              -                                          28                      ⁢                                              x                        2                                            ⁢                                              y                        6                                                              +                                          y                      8                                                                            r                    0                    8                                                  )                                      ⁢                                                   ⁢            Hexadecapole                                              (        5.2        )            In these definitions, the X direction corresponds to the direction towards an electrode in which the quadrupole potential A2 increases from zero to become more positive when V(t) is positive.
In the series of harmonic amplitudes, the cases in which the odd field harmonics, having amplitudes A1,A3,A5 . . . , are each zero due to the symmetry of the applied potentials and electrodes are considered here (aside from very small contributions from the odd field harmonics due to instrumentation and measurement errors). Accordingly, one is left with the even field harmonics having amplitudes A0,A2,A4 . . . As shown above, A0 is the constant potential (i.e. independent of X and Y), A2 is the quadrupole component of the field, A4 is the octopole component of the field, and there are still higher order components of the field, although in a practical quadrupole the amplitudes of the higher order components are typically small compared to the amplitude of the quadrupole term.
In a quadrupole mass filter, ions are injected into the field along the axis of the quadrupole. In general, the field imparts complex trajectories to these ions, which trajectories can be described as either stable or unstable. For a trajectory to be stable, the amplitude of the ion motion in the planes normal to the axis of the quadrupole must remain less than the distance from the axis to the rods (r0). Ions with stable trajectories will travel along the axis of the quadrupole electrode system and may be transmitted from the quadrupole to another processing stage or to a detection device. Ions with unstable trajectories will collide with a rod of the quadrupole electrode system and will not be transmitted.
The motion of a particular ion is controlled by the Mathieu parameters a and q of the mass analyzer. For positive ions, these parameters are related to the characteristics of the potential applied from terminals to ground as follows:                               a          x                =                              -                          a              y                                =                      a            =                                                                                8                    ⁢                    eU                                                                              m                      ion                                        ⁢                                          Ω                      2                                        ⁢                                          r                      0                      2                                                                      ⁢                                                                   ⁢                and                ⁢                                                                   ⁢                                  q                  x                                            =                                                -                                      q                    y                                                  =                                  q                  =                                                            4                      ⁢                      e                      ⁢                                                                                           ⁢                      V                                                                                      m                        ion                                            ⁢                                              Ω                        2                                            ⁢                                              r                        0                        2                                                                                                                                                    (        6        )            where e is the charge on an ion, mion is the ion mass, Ω=2πƒ where f is the RF frequency, U is the DC voltage from a pole to ground and V is the zero to peak RF voltage from each pole to ground. If the potentials are applied with different voltages between pole pairs and ground, U and V are ½ of the DC potential and the zero to peak AC potential respectively between the rod pairs. Combinations of a and q which give stable ion motion in both the x and y directions are usually shown on a stability diagram.
With operation as a mass filter, the pressure in the quadrupole is kept relatively low in order to prevent loss of ions by scattering by the background gas. Typically the pressure is less than 5×10−4 torr and preferably less than 5×10−5 torr. More generally quadrupole mass filters are usually operated in the pressure range 1×10−6 torr to 5×10−4 torr. Lower pressures can be used, but the reduction in scattering losses below 1×10−6 torr are usually negligible.
As well, when linear quadrupoles are operated as a mass filter the DC and AC Voltages (U and V) are adjusted to place ions of one particular mass to charge ratio just within the tip of a stability region, as described. Normally, ions are continuously introduced at the entrance end of the quad rupole and continuously detected at the exit end. Ions are not normally confined within the quadrupole by stopping potentials at the entrance and exit. An exception to this is shown in the papers Ma'an H. Amad and R. S. Houk, “High Resolution Mass Spectrometry With a Multiple Pass Quadrupole Mass Analyzer”, Analytical Chemistry, 1998, Vol. 70, 4885-4889, and Ma'an H. Amad and R. S. Houk, “Mass Resolution of 11,000 to 22,000 With a Multiple Pass Quadrupole Mass Analyzer”, Journal of the American Society for Mass Spectrometry, 2000, Vol. 11, 407-415. These papers describe experiments where ions were reflected from electrodes at the entrance and exit of the quadrupole to give multiple passes through the quadrupole to improve the resolution. Nevertheless, the quadrupole was still operated at low pressure, although this pressure is not stated in these papers, and with the DC and AC voltages adjusted to place the ions of interest at the tip of the first stability region.
In contrast, when linear quadrupoles are operated as ion traps, the DC and AC voltages are normally adjusted so that ions of a broad range of mass to charge ratios are confined. Ions are not continuously introduced and extracted. Instead, ions are first injected into the trap (or created in the trap by fragmentation of other ions, as described below or by ionization of neutrals). Ions are then processed in the trap, and are subsequently removed from the trap by a mass selective scan, or allowed to leave the trap for additional processing or mass analysis, as described. Ion traps can be operated at much higher pressures than quadrupole mass filters, for example 3×10−3 torr of helium (J. C. Schwartz, M. W. Senko, J. E. P. Syka, “A Two-Dimensional Quadrupole Ion Trap Mass Spectrometer”, Journal of the American Society for Mass Spectrometry, 2002, Vol. 13, 659-669; published online Apr. 26, 2002 by Elsevier Science Inc.) or up to 7×10−3 torr of nitrogen (Jennifer Campbell, B. A. Collings and D. J. Douglas, “A New Linear Ion Trap Time of Flight System With Tandem Mass Spectrometry Capabilities”, Rapid Communications in Mass Spectrometry, 1998, Vol. 12, 1463-1474; B. A. Collings, Collings, J. M. Campbell, Dunmin Mao and D. J. Douglas, “A Combined Linear Ion Trap Time-of-Flight System With Improved Performance and MSn Capabilities”, Rapid Communications in Mass Spectrometry, 2001, Vol. 15, 1777-1795. Typically, ion traps operate at pressures of 10−1 torr or less and preferably in the range 10−5 to 10−2 torr. More preferably ion traps operate in the pressure range 10−4 to 10−2 torr. However ion traps can still be operated at much lower pressures for specialized applications (e.g. 10−9 mbar (1 mbar=0.75 torr) M. A. N. Razvi, X. Y. Chu, R. Alheit, G. Werth and R. Blumel, “Fractional Frequency Collective Parametric Resonances of an Ion Cloud in a Paul Trap”, Physical Review A, 1998, Vol. 58, R34-R37). For operation at higher pressures, gas can flow into the trap from a higher pressure source region or can be added to the trap through a separate gas supply and inlet.
Recently, there has been interest in performing mass selective scans by ejecting ions at the stability boundary of a two-dimensional quadrupole ion trap (see, for example, U.S. Pat. No. 5,420,425; J. C. Schwartz, M. W. Senko, J. E. P. Syka, “A Two-Dimensional Quadrupole Ion Trap Mass Spectrometer”, Journal of the American Society for Mass Spectrometry, 2002, Vol. 13, 659-669; published online Apr. 26, 2002 by Elsevier Science Inc.). In the two-dimensional ion trap, ions are confined radially by a two-dimensional quadrupole field and are confined axially by stopping potentials applied to electrodes at the ends of the trap. Ions are ejected through an aperture or apertures in a rod or rods of a rod set to an external detector by increasing the RF voltage so that ions reach their stability limit and are ejected to produce a mass spectrum.
Ions can also be ejected through an aperture or apertures in a rod or rods by applying an auxiliary or supplemental excitation voltage to the rods to resonantly excite ions at their frequencies of motion, as described below. This can be used to eject ions at a particular q value, for example q=0.8. By adjusting the trapping RF voltage, ions of different mass to charge ratio are brought into resonance with the excitation voltage and are ejected to produce a mass spectrum. Alternatively the excitation frequency can be changed to eject ions of different masses. Most generally the frequencies, amplitudes and waveforms of the excitation and trapping voltages can be controlled to eject ions through a rod in order to produce a mass spectrum.
The efficacy of a mass filter used for mass analysis depends in part on its ability to retain ions of the desired mass to charge ratio, while discarding the rest. This, in turn, depends on the quadrupole electrode system (1) reliably imparting stable trajectories to selected ions and also (2) reliably imparting unstable trajectories to unselected ions. Both of these factors can be improved by controlling the speed with which ions are ejected as they approach the stability boundary in a mass scan.
Mass spectrometry (MS) will often involve the fragmentation of ions and the subsequent mass analysis of the fragments (tandem mass spectrometry). Frequently, selection of ions of a specific mass to charge ratio or ratios is used prior to ion fragmentation caused by Collision Induced Dissociation with a collision gas (CID) or other means (for example, by collisions with surfaces or by photo dissociation with lasers). This facilitates identification of the resulting fragment ions as having been produced from fragmentation of a particular precursor ion. In a triple quadrupole mass spectrometer system, ions are mass selected with a quadrupole mass filter, collide with gas in an ion guide, and mass analysis of the resulting fragment ions takes place in an additional quadrupole mass filter. The ion guide is usually operated with radio frequency only voltages between the electrodes to confine ions of a broad range of mass to charge ratios in the directions transverse to the ion guide axis, while transmitting the ions to the downstream quadrupole mass analyzer. In a three-dimensional ion trap mass spectrometer, ions are confined by a three-dimensional quadrupole field, a precursor ion is isolated by resonantly ejecting all other ions or by other means, the precursor ion is excited resonantly or by other means in the presence of a collision gas and fragment ions formed in the trap are subsequently ejected to generate a mass spectrum of fragment ions. Tandem mass spectrometry can also be performed with ions confined in a linear quadrupole ion trap. The quadrupole is operated with radio frequency voltages between the electrodes to confine ions of a broad range of mass to charge ratios. A precursor ion can then be isolated by resonant ejection of unwanted ions or other methods. The precursor ion is then resonantly excited in the presence of a collision gas or excited by other means, and fragment ions are then mass analyzed. The mass analysis can be done by allowing ions to leave the linear ion trap to enter another mass analyzer such as a time-of-flight mass analyzer (Jennifer Campbell, B. A. Collings and D. J. Douglas, “A New Linear Ion Trap Time of Flight System With Tandem Mass Spectrometry Capabilities”, Rapid Communications in Mass Spectrometry, 1998, Vol. 12, 1463-1474; B. A. Collings, J. M. Campbell, Dunmin Mao and D. J. Douglas, “A Combined Linear Ion Trap Time-of-Flight System With Improved Performance and MSn Capabilities”, Rapid Communications in Mass Spectrometry, 2001, Vol. 15, 1777-1795) or by ejecting the ions through an aperture or apertures in a rod or rods to an external ion detector (M. E. Bier and John E. P. Syka, U.S. Pat. No. 5,420,425, May 30, 1995; J. C. Schwartz, M. W. Senko, J. E. P. Syka, “A Two-Dimensional Quadrupole Ion Trap Mass Spectrometer”, Journal of the American Society for Mass Spectrometry, 2002, Vol. 13, 659-669; published online Apr. 26, 2002 by Elsevier Science Inc.). The term MSn has come to mean a mass selection step followed by an ion fragmentation step, followed by further ion selection, ion fragmentation and mass analysis steps, for a total of n mass analysis steps.
Similar to mass analysis, CID is assisted by moving ions through a radio frequency field, which confines the ions in two or three dimensions. However, unlike conventional mass analysis in a linear quadrupole mass filter, which uses fields to impart stable trajectories to ions having the selected mass to charge ratio and unstable trajectories to ions having unselected mass to charge ratios, quadrupole fields when used with CID are operated to provide stable but oscillatory trajectories to ions of a broad range of mass to charge ratios. In two-dimensional ion traps, resonant excitation of this motion can be used to fragment the oscillating ions. However, there is a trade off in the oscillatory trajectories that are imparted to the ions. If a very low amplitude motion is imparted to the ions, then little fragmentation will occur. However, if a larger amplitude oscillation is provided, then more fragmentation will occur, but some of the ions, if the oscillation amplitude is sufficiently large, will have unstable trajectories and will be lost. There is a competition between ion fragmentation and ion ejection. Thus, both the trapping and excitation fields must be carefully selected to impart sufficient energy to the ions to induce fragmentation, while not imparting so much energy as to lose the ions.
Accordingly, there is a continuing need to improve the two-dimensional quadrupole fields for mass filters and ion traps, both in terms of ion selection, and in terms of ion fragmentation. Specifically, for ion fragmentation in a linear ion trap, a quadrupole electrode system that provides a field that provides an oscillatory motion that is energetic enough to induce fragmentation while stable enough to prevent ion ejection, is desirable. For ion selection whether in a mass filter or in an ion trap by ejection at the stability boundary or by resonant excitation, a quadrupole electrode system that provides a field that causes ions to be ejected more rapidly, thus allowing for faster scan speeds and higher mass resolution, is also desirable.